[From nobody Thu Oct 23 22:40:12 2008 Received: from mail138.messagelabs.com (216.82.249.35) by 155M-CAHT.goldbox.com (192.168.89.65) with Microsoft SMTP Server id 8.1.291.1; Thu, 23 Oct 2008 15:17:18 -0400 X-VirusChecked: Checked X-Env-Sender: r-help-bounces@r-project.org X-Msg-Ref: server-10.tower-138.messagelabs.com!1224789434!70703372!1 X-StarScan-Version: 5.5.12.14.2; banners=-,-,- X-Originating-IP: [129.132.145.15] X-SpamReason: No, hits=0.5 required=7.0 tests=BODY_RANDOM_LONG Received: (qmail 29310 invoked from network); 23 Oct 2008 19:17:15 -0000 Received: from hypatia.math.ethz.ch (HELO hypatia.math.ethz.ch) (129.132.145.15) by server-10.tower-138.messagelabs.com with AES256-SHA encrypted SMTP; 23 Oct 2008 19:17:15 -0000 Received: from hypatia.math.ethz.ch (hypatia [129.132.145.15]) by hypatia.math.ethz.ch (8.14.1/8.14.1) with ESMTP id m9NJGMWM006374; Thu, 23 Oct 2008 21:16:39 +0200 X-Spam-Checker-Version: SpamAssassin 3.2.5 (2008-06-10) on hypatia.math.ethz.ch X-Spam-Level: X-Spam-Status: No, score=-5.3 required=5.0 tests=AWL, BAYES_00, RCVD_IN_DNSWL_MED autolearn=unavailable version=3.2.5 Received: from phil2.ethz.ch (phil2.ethz.ch [129.132.202.240]) by hypatia.math.ethz.ch (8.14.1/8.14.1) with ESMTP id m9NJG5PM005908 for <r-help@r-project.org>; Thu, 23 Oct 2008 21:16:05 +0200 Received: from moe.its.auckland.ac.nz ([130.216.12.35] helo=mailhost.auckland.ac.nz) by phil2.ethz.ch with esmtp (Exim 4.66) (envelope-from <r.turner@auckland.ac.nz>) id 1Kt5f5-0002cN-9F for r-help@r-project.org; Thu, 23 Oct 2008 21:16:06 +0200 Received: from localhost (localhost.localdomain [127.0.0.1]) by mailhost.auckland.ac.nz (Postfix) with ESMTP id C0561481EDB; Fri, 24 Oct 2008 08:15:50 +1300 (NZDT) X-Virus-Scanned: by amavisd-new at stat.math.ethz.ch Received: from mailhost.auckland.ac.nz ([127.0.0.1]) by localhost (moe.its.auckland.ac.nz [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id EFaMJwbfQYtK; Fri, 24 Oct 2008 08:15:50 +1300 (NZDT) Received: from acemm03n.foed.auckland.ac.nz (ace-104-31.auckland.ac.nz [130.216.104.31]) by mailhost.auckland.ac.nz (Postfix) with ESMTP id F0EBB481D6F; Fri, 24 Oct 2008 08:15:49 +1300 (NZDT) Received: from foedmail02n.foed.auckland.ac.nz (Not Verified[130.216.104.109]) by acemm03n.foed.auckland.ac.nz with MailMarshal (v6, 1, 8, 2172) id <B4900cd650000>; Fri, 24 Oct 2008 08:15:49 +1300 Received: from [130.216.107.232] (130.216.107.232) by foedmail02n.foed.auckland.ac.nz (130.216.104.109) with Microsoft SMTP Server id 8.1.291.1; Fri, 24 Oct 2008 08:15:49 +1300 In-Reply-To: <20130023.post@talk.nabble.com> References: <20121371.post@talk.nabble.com> <86CECCCE-91C2-4273-94FE-AE5F7868DE09@auckland.ac.nz> <20130023.post@talk.nabble.com> MIME-Version: 1.0 (Apple Message framework v752.3) Message-ID: <2F1B1AE6-68C2-4DDC-B13E-875597979CFB@auckland.ac.nz> From: Rolf Turner <r.turner@auckland.ac.nz> Date: Fri, 24 Oct 2008 08:15:48 +1300 To: Tom.O <tom.olsson@dnbnor.com> X-Mailer: Apple Mail (2.752.3) X-PMWin-Version: 3.0.1.0, Antivirus-Engine: 2.79.0, Antivirus-Data: 4.34E X-USF-Tag-Only: YES X-USF-Filter-Node: phil2.ethz.ch X-USF-Spam-Level: -- X-USF-Spam-Status: hits=-2.6 tests=BAYES_00 X-USF-Spam-Flag: NO X-USF: CC: "r-help@r-project.org" <r-help@r-project.org> Subject: Re: [R] Help finding the proper function X-BeenThere: r-help@r-project.org X-Mailman-Version: 2.1.11 Precedence: list List-Id: "Main R Mailing List: Primary help" <r-help.r-project.org> List-Unsubscribe: <https://stat.ethz.ch/mailman/options/r-help>, <mailto:r-help-request@r-project.org?subject=unsubscribe> List-Archive: <https://stat.ethz.ch/pipermail/r-help> List-Post: <mailto:r-help@r-project.org> List-Help: <mailto:r-help-request@r-project.org?subject=help> List-Subscribe: <https://stat.ethz.ch/mailman/listinfo/r-help>, <mailto:r-help-request@r-project.org?subject=subscribe> Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset="windows-1252"; format=flowed; delsp=yes Sender: <r-help-bounces@r-project.org> Errors-To: r-help-bounces@r-project.org Return-Path: r-help-bounces@r-project.org X-MS-Exchange-Organization-OriginalArrivalTime: 23 Oct 2008 19:17:18.2876 (UTC) X-MS-Exchange-Organization-AuthSource: 155M-CAHT.goldbox.com X-MS-Exchange-Organization-AuthAs: Anonymous X-MS-Exchange-Organization-OriginalSize: 7290 X-MS-Exchange-Organization-Recipient-Limit-Verified: True On 24/10/2008, at 1:37 AM, Tom.O wrote: > > Ok, I'll try to be clearer. I'll start from the beginning. I have = > a set of > samples that I'm going to use to model a proxy for a common = > property. This > property is that the samples are either in a "quiet" or "chaotic" = > state. > Both the quiet and chaotic state is modelled to be normal = > distributed. So > these samples are believed to be from a mixture of univariate normal > distributions. But some samples do not have this property and are = > believed > only to come from a "quiet" state and is believed to be from a = > univariate > normal distribution. > > > What I also know or assume to know is that when the samples that = > are drawn > from a mixture distribution change between distributions they do that > simultaneously or near simultaneously. So each sample have a = > probability "p" > of being in either state. But since some samples are from a univariate > distribution and some of the samples that are from a mixture = > distribution > don=92t show a clear change they are no good at estimating the overall > probability of being in the "quiet" or "chaotic" state. > > What I'm looking for is the combination of samples that would give = > med the > best proxy to model the overall state, some sort of optimizer. > > > So hopefully this clarifies my problem. Yes it does. Bivariate has nothing to do with your problem. Mixtures has everything to do with it. Essentially your problem is testing k=3D2 versus k=3D1 where k is the number of components in the model. I believe there is a substantial literature about this; you could start with G. J. McLachlan and K. E. Basford = ``Mixture Models: Inference and Applications to Clustering'', Dekker, New = York, 1988. I believe that the story is roughly that the test you want can be = carried out via a likelihood ratio test, but that the null distribution of = the test statistic is problematic. It is ***not*** asymptotically chi-squared. As far as I know the actual null distribution is impossible to determine analytically, hence one is left with a single option: Bootstrapping. The mixtools package on CRAN may provide the facilities you need; = there are other packages on CRAN which relate to mixtures. In particular look at Peter MacDonald's mixdist package. I would conjecture (I haven't = looked) that the latter package would provide useful pointers to the literature, including Peter's own substantial contributions. HTH cheers, Rolf Turner ###################################################################### Attention: = This e-mail message is privileged and confidential. 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